The problem of unsteady-state liquid flow across overflow devices of various shapes has been investigated. Dimensionless efflux times to evacuate a given amount of liquid from an upstream vessel or basin through an overflow conduit or weir as a function of dimensionless height of the liquid crest were computed for four specific overflow device shapes: rectangular, circular, parabolic and triangular. Analytical expressions were developed for this purpose in all cases except circular. Generalized comparison charts were developed for the cases of (1) equal flow areas of the overflow devices and (2) equal maximum flow capacities. Two examples illustrating application of the equations and charts developed in this paper to loss prevention scenarios are also presented.